Atletico had given Alvarez until Sunday to decide whether he wanted to remain in Madrid or consider a move to Arsenal. However, no formal decision has emerged and there is still uncertainty over where the Argentina international will be playing after Tuesday's deadline.
The striker returned to first-team training on Sunday after missing several days last week. Alvarez was absent because of illness and trained separately on Saturday while Atletico recorded a 3-1 victory away to Sevilla.
Club officials have described Alvarez as "struggling" and "confused" by the situation, but his return to the group has provided no definitive indication that he has decided to stay.
Alvarez's preferred destination has been Barcelona, with an agreement reportedly reached over personal terms. However, Atletico have firmly rejected the possibility of selling him to their La Liga rivals.
Atletico CEO Miguel Angel Gil Marin has made it clear that the club does not want to strengthen Barcelona, effectively closing the door on a move to the Catalan giants during this transfer window.
That has left Arsenal as the main alternative if Alvarez decides to leave Madrid. Atletico are understood to be prepared to sanction a transfer if their valuation of around 128 million pounds, or 150 million euros, is met.
Arsenal, however, have long been aware of Alvarez's reluctance to return to the Premier League. The striker is understood to have reservations about joining the Gunners, particularly if he sees the move as merely a route towards a future transfer to Barcelona.
There has nevertheless been a late development, with Arsenal making another attempt to convince Alvarez to join Mikel Arteta's side before the window closes.
One possible compromise being discussed would involve a future Barcelona-specific release clause, although Arsenal are understood to be considering whether such an arrangement makes financial sense.
For now, Atletico are keeping their cards close to their chest. Alvarez trained with his team-mates on Sunday and remains part of the squad for the next La Liga fixture against Athletic Club.